go your own way
Anna and Castiel have one of the more interesting relationships in the series, in my humble opinion. From the very beginning there's a certain dynamic between the two, and although their on-screen time together is brief there is always a sense of a history between them. And it's that history I think that allows Anna to have such an influence over Castiel on his journey towards disobedience. (Though without her things may have turned out the same for Castiel. God knows Dean was bad enough as it was...)
But on the subject of their "history," the specifics of what their life was like before Anna's fall is pretty much unknown. Anna made mention of the fact that Castiel was her subordinate in their garrison on Earth, and knowing Castiel he probably cared for her in the same way innocent he did all angels. But regardless of the past, he didn't question his orders when sent to execute the fallen Anna after she became a liability in the war against Hell. When he told Anna he was sorry for what he had to do she made it quite clear that she didn't believe him, because he - being a good little soldier - probably had no idea what regret even was.
However, despite Anna's disregard for Castiel's apology, I still think that was a very big moment for him that helped set the stage for future interactions. When Anna turned to kiss Dean goodbye the camera cut to a close-up of Castiel and he had this look on his face (as shown in the picture to the right).
Now, I'm not saying this was necessarily a "Damn I love you Anna why you be kissin' on Dean?" look, but it was still important; even if Castiel didn't have the emotional depth to understand what was going on, he saw an angel that he once held in very high regard being blatantly human. What he felt at that moment could have been jealousy, curiosity, or even absolutely nothing, but at the very least he started thinking.
And even if she was initially sceptical over his emotional capacity and they remained on opposing sides, after Anna regained her grace she seemed to have a great deal of faith in Castiel. This was most clearly seen in the simple fact that she approached him to talk, knowing full well he was under orders to kill her. Castiel lived up to that trust, even if that in and of itself was disobedience. And I think Anna, with her human family dead and her heavenly family out to kill her, really needed to take the chance; watching how she spoke to Castiel, it wasn't as much that she needed an ally as much as she needed a friend. Except Anna pushed too hard with her talk of disobedience and Castiel lashed out at her, telling her to go away. Now I'm not going to lie, I'm still not sure if he was angry at her for suggesting it, or himself for considering it.
When Castiel was finally faced with the reality that maybe God wasn't giving the orders anymore and had no choice but to think about disobedience, it probably helped a great deal to know there was an angel in his corner. Except even then Anna seemed more concerned with Castiel's acceptance than his allegiance, and when she reached out and was rejected she started to walk away. But after he stopped her to plead for her to tell him what to do and she refused it didn't mean that she was in turn rejecting him - the whole idea of disobedience was for Castiel to think for himself. It was just tough love - pushing him out of the nest and hoping he could fly.
In fact, Anna watched over Castiel quite closely, and not long after she rejected his requests for orders she committed a very serious crime for his sake - killing Uriel to save his life. When she did that, she told Uriel, who denied the existence of God or anything else, that "there's still me." What I truly believe she meant by that is that even if God had abandoned them all, she was still there for Castiel. Her desire to watch out for Castiel was also obvious when she became quite upset when he was dragged back to Heaven for considering disobedience, and again I don't think it was just because he was an ally in the fight against the coming apocalypse.
Then whatever happened to Castiel up in Heaven set him firmly back on the straight and narrow, and although he didn't exactly hand her over, he stood back and let Anna be taken. Castiel finally carried out his orders, except there was a big difference between when he was first sent to kill her and when she was finally apprehended - this time he finally was sorry, and when the other angels took her away he couldn't even look her in the eye. Anna had clearly left her mark on him.
Half a season later, Anna managed to escape from angel prison with the goal of killing Sam and stopping the apocalypse, but this put her and Cas back on opposing sides. Castiel had finally grown enough emotionally to choose his friends over his duty, but although this was good for Sam it was too late for Anna. The last time the would ever see each other Castiel threatened to kill her if she came after Sam, and although the show never stated it explicitly it was fairly obvious: Castiel had finally become what she wanted him to be, but it only lead him to turn against her once again.
So are they meant to be?
I also believe that regardless of whether or not you believe in the possibility of squishy feelings between them, Anna was definitely good for Castiel. The most obvious is that she served as a voice for the doubts he had that he could never openly admit to himself. Moreover, when angels think of falling they think of Lucifer, but here was Anna - an angel who committed the worst crime possible but did so for entirely different reasons. That Castiel could follow her example shows the depth of his feelings for her, whether it's love or just plain old respect. And Castiel, in turn, was good for Anna, giving her someone when she was at her most alone.
Though there's the certain problem of timing. And the fact that Castiel is not the most in-touch person when it comes to his emotions. Oh, and we can't forget that he kind of betrayed Anna, and eventually left her for the Winchesters. And of course, Michael kind of killed Anna...
But it's Supernatural so you never know!